The pavement in our driveway is sinking. We have two heavy
cars(Jeep and an SUV), we drive over these pavement everyday and
I'm afraid it may crack very soon.

I've already poured at least two bags of sand in the hole
thinking it would stop it from sinking...that didn't work. I
then emptied another bag of top soil into it to no avail. When it
rains, the sand and dirt just get washed away out of a small
space/crack at the end of the driveway. It's getting worse and
I'm out of ideas on how to stop it from sinking further.

Attached are some pictures. From one of the picture, you can see
one pavement is about 2+inches below the others. I'm almost
afraid to drive over them...but I've no other way.

It's difficult to say tell from here ....
There may be an issue with the sub-base under the slab not properly done.... causing settling .
Also considering the number of control cuts and the slope of the driveway ... it looks as though those control cuts had never been caulked. You may have rain water getting in and undermining the base under the slab.

You might check the Yellow pages for a company that does " Mudjacking" to come and raise the sections.

It looks as though there may be some patching of the concrete in certain areas as well.

That could happen if/because the ground underneath is water-logged from a leak in either a water supply line or a waste water/drain line. Surface water might not show up on a daily basis, but only when rainwater is added to the absorbency demand load.

Or......it could happen if the ground/fill under the drive is comprised of clay. Not very absorbent and prone to somewaht unpredictable behavior.

Something is amiss underneath the slab and simply mud-jacking it....may not offer a long term result. Impossible to say from here.

Mud-jacking *might* work if the problem is/was a lack of proper fill or improper compaction of the fill before pouring the drive. Again, impossible to say from here.

The city/local health department... should/might have records showing where the city supply and waste lines run on your property. I guess I'd check that out first. If there is a leaking supply/potable-water line under there, it wouldn't necessarily show on your meter because the leak could be prior to the meter. Ever see those pics on the tee-vee news where cavernous holes open up in streets because of water main leaks?

Same thing can happen if your line to the sewer (or septic tank) is leaking. Slowly but surely it can/will erode the soil away.

You obviously have plenty of places for water to get under your slabs and erode the base. This will continue to get worse as the rains persist! You can try mudjacking and cement patching but, in the long run they are "bandaids" at best. Take it from an old cement finisher. When the driveway gets to the point that it is cracking under the vehicle weight its time to replace the concrete. All the money you spend on "bandaids" could go to replacing the bad concrete with slabs that are new with the properly compacted drainage base. I would suggest getting some prices from reputable cement contractors and maybe only some of the slabs would need replaced instead of the entire driveway. Good Luck.